Weak stability for integro-differential inclusions of diffusion-wave type involving infinite delays

Thanh-Anh  Nguyen; Dinh-Ke  Tran; Nhu-Quan  Nguyen

doi:10.3934/dcdsb.2016114

Article Contents

2016, Volume 21, Issue 10: 3637-3654. Doi: 10.3934/dcdsb.2016114

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Weak stability for integro-differential inclusions of diffusion-wave type involving infinite delays

1.
Vietnam Education Publishing House, 81 Tran Hung Dao, Hanoi
2.
Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy, Cau Giay, Hanoi
3.
Department of Mathematics, Electric Power University, 235 Hoang Quoc Viet, Hanoi

Received: October 31, 2015

Revised: July 31, 2016

Published: November 2016

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Abstract

We deal with the Cauchy problem associated with integro-differential inclusions of diffusion-wave type involving infinite delays. Based on the behavior of resolvent operator associated with the linear part, an explicit estimate for solutions will be established. As a consequence, the weak stability of zero solution is proved in case the resolvent operator is asymptotically stable.

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Mathematics Subject Classification: Primary: 35B35, 37C75; Secondary: 47H08, 47H10.

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